Re: Triangularize Matrix for Newmark method Keff=L^TDL

• To: mathgroup at smc.vnet.net
• Subject: [mg57068] Re: [mg57048] Triangularize Matrix for Newmark method Keff=L^TDL
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Sat, 14 May 2005 04:58:05 -0400 (EDT)
• References: <200505130244.WAA24007@smc.vnet.net>
• Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

```If you look at the help for LUDecomposition, you will notice that it
isn't necessary to break down the resulting matrix into L and U if you
use LUBackSubstitution (shouldn't it be called
LUForwardThenBackSubstition? ... ). LUBackSubsitution will also take
care of the pivoting (row swapping).
The same help file does give functions to obtain L and U, but I don't
think those take care of the row swaps.

On 5/12/05, athanatos <athanatos at wayne.edu> wrote:
> Am implementing the Newmark method, need to triagularize the effective stiffness matrix, so need to get the lower triangular part "L" of the LU Decomposition. However, Mathematica gives the LU decomposition as one matrix?? and it took some effort to extract the L part as part of a test, had to construct a matrix by hand, with negative entries to cancel out the upper part to zero, then add this to the identity. Is there an easier way to do this??? Actually, went ahead and also extracted the U(upper triangular matrix) and then multiplied them L*U together to see if I got back the original matrix, and almost did, except the second and third rows were interchanged. Can send along the nb via email. thanks in advance for any help.
>
>

--
Chris Chiasson
http://chrischiasson.com/
1 (810) 265-3161

```

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